What is the principal value of cos^-1(- (√(2))/2)?

Inverse Trigonometric Functions · Question 50 of 120

Question 50

MediumOriginal question

What is the principal value of $\cos^{-1}\left(- \frac{\sqrt{2}}{2}\right)$ ?

- \frac{\pi}{4}

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\frac{\pi}{4}

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\frac{3 \pi}{4}

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\frac{5 \pi}{4}

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

Find the angle $\theta$ in the branch $[0, \pi]$ with $\cos \theta = - \frac{\sqrt{2}}{2}$ .
That angle is $\frac{3 \pi}{4}$ .

Worth noting

A negative input to $\cos^{-1}$ gives an angle between $\frac{\pi}{2}$ and $\pi$ : $\pi - \frac{\pi}{4}$ .

Ten questions from Inverse Trigonometric Functions, at your own pace.

Ten questions from Inverse Trigonometric Functions, at your own pace.